改进广义移动最小二乘近似的无网格法

无网格法是求解微分方程定解问题的一种新数值方法.移动最小二乘近似只要求近似函数在各节点处的误差的平方和最小,对近似函数导数的误差没有任何约束.而广义移动最小二乘近似要求近似函数及其导数在所有节点处的误差的平方和最小.为了降低计算工作量,本文构造了要求近似函数在全部节点处和任意阶导数在部分节点处误差的平方和最小的改进广义移动最小二乘近似.数值计算显示本文提供的方法关于函数值和各阶导数值都具有很高的精度.     

弹性静力问题的无网格弱-强形式结合法

基于改进的移动最小二乘(MLS)二阶导数近似,建立了一种求解弹性静力问题的无网格弱-强形式结合法(MLS-MWS)。该方法采用节点离散求解域,通过MLS构造形函数,将求解域划分为边界域和内部域,并分别使用控制方程的局部弱形式和强形式来建立离散系统方程。对强形式中涉及的近似函数二阶导数计算,提出了一种将其转化为求两次一阶导数的方法,与传统方法相比,该方法计算简单、精度高。MLS-MWS法结合了弱、强形式无网格法的优点,Neumann边界条件容易满足,并且只需在边界区域进行积分。文中应用该方法分析了两个弹性力学平面问题,分析结果表明本文方法具有良好的精度和收敛性。     

加权最小二乘无网格法

在最小二乘法和移动最小二乘近似的基础上提出了加权最小二乘无网格法．该方法除节点外又引入了一些辅助点，控制方程在所有节点和辅助点处的残差用最小二乘法予以消除，边界条件用罚函数法引入．另外对移动最小二乘近似进行了改进，并给出了最小二乘法中泛函的简化格式，因而提高了计算效率．与配点法相比，新方法精度高，稳定性好，并且系数矩阵是对称正定矩阵．与Galerkin法相比，该方法不需要进行高斯积分，因而计算量小．算例表明该方法具有效率高、精度高和稳定性好等优点，并且易于实现．     

瞬态热传导问题的加权最小二乘无网格法

加权最小二乘无网格法是一种基于节点信息的纯无网格法,该方法使用最小二乘法建立系统的变分原理,通过移动最小二乘法构造近似函数,控制方程在节点处的残量使用最小二乘法予以消除,边界条件通过罚函数法引入。本文推导了瞬态热传导问题的加权最小二乘无网格计算格式,编制了相应的计算程序,算例结果表明,该方法具有精度高、前后处理简单的优点,是一种高效的的新型无网格法。     

一种求解三维声腔声压分布问题的无网格法

利用传统有限元法求解声压分布问题常常受到污染误差和色散误差的困扰。加权最小二乘无网格法（MWLS）是一种基于移动最小二乘（MLS）近似的无网格方法,求解声腔声压分布问题具有低色散、高精度的特点。然而传统的MLS近似有时容易产生病态矩阵,利用加权正交基函数构建改进的移动最小二乘（IMLS）近似,得到的系统方程为非病态的。本文基于改进的加权最小二乘无网格法（IMWLS）求解三维声腔内部声压分布。计算得到的声压分布和声压频响曲线都与参考值十分吻合,峰值误差和污染误差都比FEM的小,计算成本相比无单元伽辽金法显著降低。计算结果表明IMWLS相比传统的FEM,能在更高的频段内达到高精度,并且相比EFGM能大幅提高计算效率。     

基于径向基函数的加权最小二乘无网格法

径向基函数插值是一种新型的无网格插值方法,具有形式简单、空间维数无关等优点.这种插值方法具有δ函数的性质,易于满足本质边界条件,且插值函数的导数求解过程比通常的移动最小二乘插值(MLS)简单,精度也较高.另一方面,通过加权最小二乘法离散控制方程不需要积分,具有效率高,精度高等优点.本文试图将两者的优点结合起来,发展一种...     

用无网格局部Petrov-Galerkin法分析非线性地基梁

利用无网格局部Petrov-Galerkin法求解了非线性地基梁。在Petrov-Galerkin方法中，采用移动最小二乘（MLS）近似函数作为场主量挠度的试函数并取移动最小二乘近似函数中的体验函数作为近似场函数的加权函数，采用罚因子法施加本质边界条件。文末给出了两个计算实例，算例的结果表明，Petrov-galerkin法不仅能成功地分析线性地基梁，而且也适用于解非线性地基梁，在分析非线性地基梁时具有收敛快，稳定性好的优点。     

基于核重构思想的最小二乘配点型无网格方法

介绍重构核点法的基本原理和近似函数的构造方法，并基于核重构思想，应用配点法和最小二乘原理，离散微分方程，建立求解的代数方程，提出了一种基于核重构思想的最小二乘配点型无网格方法．与一般配点法相比，该方法的系数矩阵是有对称正定的，计算精度高，稳定性好．该方法的实施不需要背景网格，不需要进行高斯积分，与Galerkin法相比，具有计算量小、边界条件处理简单的特点，是一种真正的无网格法．对该方法构造过程中的近似函数及其导数的计算、修正函数的计算及方法的实现等问题进行了探讨．文中结合若干典型算例，检验了该方法的有效性．     

无网格全局介点法

提出了一种新型无网格法,即无网格全局介点(MGIP)法。该方法采用移动最小二乘核近似来构造形函数,有利于提高数值方法的计算稳定性,而且算法更为简单。该方法需要引入全局介点进行数值离散,基于有限点的广义变分法导出求解系统方程,并采用罚系数法来保证边界条件,数值实现较为简洁。数值算例结果表明:MGIP法的计算耗时不到无网格局部彼得洛夫-伽辽金法的1%,具有较高的计算效率;相比于一般配点法,本文方法的计算稳定性更好,计算精度更高。     

求解Helmholtz方程基于核重构思想的最小二乘配点法

基于核重构思想构造近似函数，将配点法和最小二乘原理相结合对微分方程进行离散， 建立了Helmholtz方程的最小二乘配点格式，并分别研究了Helmholtz方程的波传播问题和 边界层问题. 通过数值算例可以发现，给出的数值计算结果非常接近于精确解，计算精度明显高于SPH 法的数值结果，且随着节点数目的增加，其精确度越来越高，具有良好的收敛性.     

Preface: Current research progress on mechanics of high speed rail

The construction and operation of high-speed rail（HSR）grid within the past two decades in China,in terms of the scale,may be possibly comparable to any national-wide construction in the history of China,even the Great Wall.By counting railways with commercial train service at the speed of200 km/h,China has the world’s longest HSR network with over 19 369.8 km of track in service today and this number     

ACTA MECHANICA SINICA 2014 ANNUAL SUBJECT INDEX

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人造地震动合成中的位移误差分析

三角函数级数法是合成人工地震动常用算法之一,但是通过对加速度积分求取位移时,却存在与零线漂移相类似的位移漂移现象。     

Hermitian space-time finite elements for estuarine mass transport

Space-time finite element solutions of the convection–dispersion equation using higher-order nodal continuity and Hermitian polynomial shape functions are described. Five separate elements ranging from a complete linear element with C^0,0 nodal continuity to a complete first-order Hermitian element with C^1,1 nodal continuity are subjected to detailed analysis. Wave deformation analyses identify the source of leading or trailing edge oscillations, trailing edge oscillations being the major source of difficulty. These observations are confirmed by numerical experiments which further demonstrate the potential of higher-order nodal continuity. The performance of the complete first-order Hermitian element is quite satisfactory and measurably superior to the linear element.     

Rainwater rivulets on a cable subject to windFilets d'eau de pluie sur un câble soumis au vent

Rainwater rivulets appear on inclined cables of cable-stayed bridges when wind and rain occur simultaneously. In a restricted range of parameters this is known to cause vibrations of high amplitudes on the cable. The mechanism underlying this effect is still under debate but the role of rainwater rivulets is certain. We use a standard lubrication model to analyse the dynamics of a water film on a cylinder under the effect of gravity and wind load. A simple criterion is then proposed for the appearance and position of rivulets, where the Froude number is the control parameter. Experiments with several geometries of cylinder covered with water in a wind tunnel show the evolution of the rivulets with the Froude number. Comparison of the prediction by the model with these experimental data shows that the main mechanism of rivulet formation and positioning is captured. To cite this article: C. Lemaitre et al., C. R. Mecanique 334 (2006).     

Cristallisation par onde acoustique : le cas de l'héliumCrystallization by acoustic waves: the case of helium

We establish a theoretical model to explain the nucleation of a crystal of helium by an acoustic over-pressure. We explain the interfacial laws for this ultra-fast cristallization, close to the sound speed. Assuming spherical symmetry and taking into account the experimental data, we recover the dynamics of the growth and melting during an over-pressure impulse. To cite this article: M. Ben Amar et al., C. R. Mecanique 331 (2003).     

Structure initiale et propriétés de liquéfaction statique d'un sableInitial structure and static liquefaction properties of sand.

Based on the use of two different preparation procedures for reconstituting triaxial samples of sand, i.e. wet tamping and dry pluviation, significant differences in associated mechanical behaviour are observed on a reference sand with respect to the phenomenon of ‘static’ liquefaction. Wet tamping favours the initiation of liquefaction instability, whereas dry pluviation favours a more stable behaviour, less susceptible to liquefaction. Microscopic observation of corresponding sand specimens allows us to identify two well differentiated structures, i.e., for wet tamping, an irregular structure with predominance of aggregates (aggregated grains) and macropores, very contractant and unstable and, for dry pluviation, a more regular structure, without macropores, more dilatant and more stable. These observations show the importance of further characterization, based on the introduction of appropriate parameters, of the initial structure of sandy materials, strongly dependant upon their mode of formation (natural or artificial). To cite this article: N. Benahmed et al., C. R. Mecanique 332 (2004).     

INFORMATION FOR CONTRIBUTORS

Contributions： The Journal, Acta Mechanica Solida Sinica, is pleased to receive papers from engineers and scientists working in various aspects of solid mechanics. All contributions are subject to critical review prior to acceptance and publication.     

The 7th International Conference on Fluid Mechanics May 24-27,2015,Qingdao,China

正http://www.icfm7.org First Announcement and Call for PapersThe objective of International Conference on Fluid Mechanics(ICFM)is to provide a forum for researchers to exchange new ideas and recent advances in the fields of theoretical,experimental,computational Fluid Mechanics as well as interdisciplinary subjects.It was successfully convened by the Chinese Society of Theoretical and Applied Mechanics(CSTAM)in Beijing(1987,